That triumph made her only the second woman ever to win a medal in both downhill and Super-G at two separate World Championships, having also achieved the feat in 2019; American Lindsey Vonn (2007, 2009) is the only other skier to have done so.
Maria Walliser was the last Swiss world champion in women's downhill.
Two-time defending champion Ilka Stuhec of Slovenia could only finish 14th.
Suter, the defending downhill World Cup Crystal Globe holder, had won silver in this event in Åre, Sweden, behind Stuhec in 2019.
She was always inside the time of early leader Breezy Johnson of the United States, holding her tuck and racing line well.
The 26-year-old crossed the line in 1:34.27, some nine-tenths faster than Johnson.
"My run was really good, I did what I wanted to ski, what I needed to give me the space and take the speed with me," Suter told FIS.
She added that her Super-G silver medal gave her confidence: "More than I first thought, I always knew in downhill I had more chances and then I started with a silver medal in Super-G.
"Today was a new day, I felt really good in the morning, and I knew I did everything I could."
Weidle was 0.2 seconds behind in second, having looked like potentially threatening Suter for gold.
"It's still kind of unbelievable, I'm just happy," Weidle told Eurosport after the race. "I was hoping for a medal, it was my biggest goal today.
"While I was racing I really felt good, no big mistakes. I knew I could be fast, Corinne was just faster."
Gut-Behrami – who was ahead of Suter's time for most of the run until an error around midway through the run costing her time in the final third – finished 0.17 seconds further back.